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The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

A detailed study of the elementary excitations of an electron gas confined to a tubule system is presented. The system could consist either of a single cylindrical tubule or of several tubules sharing a 0 common axis. Graphene tubules with a radius as small as 11 A have been recently realized. Essential features revealed from this study are expected to be common to the graphene tubules. The dielectric function of the quasi-one-dimensional (1D) tubular system has been evaluated exactly within the random-phase approximation, where both the intrasubband and the intersubband excitations are included. The angular momentum (L) is conserved in the tubule system. The excitations, e.g. , plasmons, of different L's are thus mutually decoupled. At any given L, only a small number of plasmon branches exist, every one of which can be studied systematically. Intertubule interaction for coaxial tubules has been included. The coupling among coaxial tubules adds unique features that distinguish the tubules from other quasi-1D systems.

This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.

This paper investigates strain effects on the electronic properties of single-layer and bilayer graphene using a first-principles method. The deformation significantly alters energy dispersion, band overlap, band gap, and the band edges of graphenes. Fermi velocity behaves both linearly and nonlinearly with the strains, depending on the types of deformation and the direction of the Fermi velocity. In bilayer graphene, the uniaxial strain enhances the band overlap by 2 orders of magnitude. A semimetal–insulator transition occurs when bilayer graphene is under a compressive uniaxial strain along the zigzag chain direction. These strain-dependent results are useful for acquiring the intralayer and interlayer atomic relations or Slonczewski–Weiss–McClure parameters. The intralayer coupling γ0 under the H-strain and interlayer couplings γ1, γ3, and γ4 under the P-strain decrease dramatically as the strain increases. Nevertheless, interlayer couplings vary more slowly with the H-strain than the P-strain.

In this paper, we calculated the dielectric function, the loss function, the magnetoplasmon dispersion relation and the temperature-induced transitions for graphene in a uniform perpendicular magnetic field B. The calculations were performed using the Peierls tight-binding model to obtain the energy band structure and the random-phase approximation to determine the collective plasma excitation spectrum. The singleparticle and collective excitations have been precisely identified based on the resonant peaks in the loss function. The critical wave vector at which plasmon damping takes place is clearly established. This critical wave vector depends on the magnetic field strength as well as the levels between which the transition takes place. The temperature effects were also investigated. At finite temperature, there are plasma resonances induced by the Fermi distribution function. Whether such plasmons exist is mainly determined by the field strength, temperature, and momentum. The inelastic light scattering spectroscopies could be used to verify the magnetic field and temperature induced plasmons. Keywords: graphene · Landau level · electronic excitation · random phase approximation · magnetic field · tight-binding model † E-mail: ggumbs@hunter.cuny.edu * E-mail: mflin@mail.ncku.edu.tw 1 Graphene, a flat monolayer of carbon atoms with a honeycomb lattice, is the basic building block for other graphitic materials. It is famous for the linear energy dispersion around the zero Fermi energy, where the electrons can travel thousands of interatomic distances without scattering. Based on the high electron mobility, graphene is a popular candidate for the production of future nanoelectronic elements, such as ballistic transistors, the entire π-magnetoelectronic structure at realistic magnetic field strengths can be solved. The number of charge carriers per area is self conserved during our calculations. Therefore, the accuracy of our results is not constrained by either the energy range or the magnetic field. In the random-phase approximation (RPA), 2 the complete structure of the dielectric function was determined. The single-particle and collective excitations can be precisely identified according to the divergences in the loss function ℑm(−1/ǫ(q, ω)), where q is the in-plane wave vector and ω is the frequency. It should be noted that our discussion is within the condition that q is much smaller than the reciprocal-lattice vector, and the local-field effects 30,31 are neglected in our calculation.The group velocities of the magnetoplasmons in the long wavelength limit are typically positive, and then decrease to negative values as the wave vector is increased. The critical momentum for plasmon damping to occur is clearly established. Our calculations show that this critical wave vector has a strong dependence on the field strength as well as the levels between which the transition takes place. The temperature effects were also investigated and are reported in detail below. We found that the intra-Landau level t...

The low-frequency optical excitations of AA-stacked bilayer graphene are investigated by the tight-binding model. Two groups of asymmetric LLs lead to two kinds of absorption peaks resulting from only intragroup excitations. Each absorption peak obeys a single selection rule similar to that of monolayer graphene. The excitation channel of each peak is changed as the field strength approaches a critical strength. This alteration of the excitation channel is strongly related to the setting of the Fermi level. The peculiar optical properties can be attributed to the characteristics of the LL wave functions of the two LL groups. A detailed comparison of optical properties between AA-stacked and AB-stacked bilayer graphenes is also offered. The compared results demonstrate that the optical properties are strongly dominated by the stacking symmetry. Furthermore, the presented results may be used to discriminate AABG from MG, which can be hardly done by STM